Applied Math · Mathematics & Statistics
Dynamical Systems
The newest papers in Dynamical Systems that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
56 papers, from 8 September 2026 to 5 November 2026: 56 arXiv preprints.
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Newest papers
Data-driven discovery of intrinsic Lie point symmetries of differential equation systems
Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations…From hydrological laws to catchment models: A process-based model matches deep-learning accuracy on three continents
Dooge asked whether hydrology has laws at the catchment scale.Substrate hypergraph cycles: unique steady states and persistence for every enzyme assignment; oscillations enabled by enzyme sharing
We associate a directed substrate hypergraph with an enzymatic reaction system.Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps
The spring-loaded inverted pendulum (SLIP) describes the center-of-mass (COM) motion of runners but has no trunk.A Universal Policy Wrapper With Guarantees
Many control tasks require driving the system into a prescribed goal set and subsequently keeping it there.Efficient Closure Learning in Dynamical Systems: A Comparison of Data-Assimilated and Embedded Approaches
Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require…Nonreciprocal Spherical Attention and Retrieval: Sharp Coarsening Clocks and Certified Score Correction
We develop nonreciprocal spherical attention as a mathematical framework for coarsening and compressed nearest-neighbor retrieval.Learning hidden-state dynamics from unpaired snapshots with lift-project SDEs
Many systems are observed only through unpaired snapshots, with population samples available at each time point but no correspondence between samples at different times.Generative SDEs with Trainable Diffusion and Density-Based Losses
We develop a divergence-kernel method for jointly optimizing neural SDE drift and diffusion fields and the initial Gaussian distribution, using losses that depend directly on the terminal density.Analog and hybrid computing in the 21st century
Analog computers solve problems through physical representations of mathematical variables and relations, often using the dynamics of electronic circuits and their associated signals.Learning Kolmogorov Backward Operators for Spectral Analysis and Forecasting: A Data-Driven Variational Galerkin Framework
For a time-homogeneous Markov process, the fixed-lag solution operator \( (T_τf)(x)=\mathbb E[f(X_{t+τ})\mid X_t=x] \) of the Kolmogorov backward equation evolves observables linearly and…RC Prediction: A Python Package for Parameter-Aware Reservoir Computing
A nonlinear dynamical system can be characterized by the autonomous evolution of its state in time and its dependence on system parameters.Spontaneous Spirals in Spatial Systems
Several chemical and biological systems produce spontaneous spirals in their dynamical behavior, such as the Belousov-Zhabotinsky reaction in chemistry and the slime mold Dictyostelium in biology.Balanced Active Subspaces for Optimal Control via Trajectory Optimization
The curse of dimensionality associated with solving the Hamilton-Jacobi-Bellman equation for the value function remains a key obstacle for real-time optimal feedback control of high-dimensional…Extrapolating learned dynamics across bifurcations based on generalized synchronization
Predicting dynamics across bifurcations by extrapolating trained models is crucial in diverse fields of physics.Global Convergence of Detailed Balanced Mass Action Systems
We give a self-contained proof that, for a finite detailed balanced mass-action system with positive rate constants, each positive stoichiometric compatibility class contains exactly one positive…SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood.On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials
We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $θ(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has…Improved Training of Strong Stochastic Flow Maps
Stochastic flow maps promise few-step sampling of stochastic differential equations (SDEs) by learning to directly jump between times along the solution path, yet training these models to learn this…The Dynamics of Collapse and Recovery in Clustered Federated Learning
Clustered federated learning (CFL) can suffer from cluster collapse.